Multi-robot active target tracking with distance and bearing observations

In this paper, we study the problem of optimal trajectory generation for a team of mobile robots tracking a moving target using distance and bearing measurements. Contrary to previous approaches, we explicitly consider limits on the robots' speed and impose constraints on the minimum distance at which the robots are allowed to approach the target. We first address the case of a single sensor and show that although this problem is non-convex with non-convex constraints, in general, its optimal solution can be determined analytically. Moreover, we extend this approach to the case of multiple sensors and propose an iterative algorithm, Gauss-Seidel-relaxation (GSR), for determining the set of feasible locations that each sensor should move to in order to minimize the uncertainty about the position of the target. Extensive simulation results are presented demonstrating that the performance of the GSR algorithm, whose computational complexity is linear in the number of sensors, is indistinguishable of that of a grid-based exhaustive search, with cost exponential in the number of sensors, and significantly better than that of a random, towards the target, motion strategy.